Let L be the set of all lines in a plane and let R be the relation on L defined by \(R = \{(L_1, L_2) : L_1 \text{ is perpendicular to } L_2\}\). Then R is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → symmetric but neither reflexive nor transitive
Not reflexive: no line is perpendicular to itself, so \((L_1, L_1)\) is never in R.
Symmetric: if \(L_1\) is perpendicular to \(L_2\), then \(L_2\) is perpendicular to \(L_1\).
Not transitive: let \(L_1\) be the x-axis, \(L_2\) the y-axis and \(L_3\) the line \(y = 1\).
\(L_1\) is perpendicular to \(L_2\)
\(L_2\) is perpendicular to \(L_3\)
\(L_1\) is parallel to \(L_3\), not perpendicular
So R is symmetric but neither reflexive nor transitive.